Question

Which of the following values of x do not satisfy the inequality x² – 3x + 2 > 0 at all.

(a) 1 < \(x\) < 2 

(b) – 1 > \(x\) > – 2 

(c) 0 < \(x\)< 2 

(d) 0 > \(x\) > – 2

Answer 1

(a) 1 < x < 2

x² – 3\(x\) + 2 > 0 ⇒ (\(x\) – 2) (\(x\) – 1) > 0 

⇒ (\(x\) – 2) > 0, (\(x\) – 1) < 0 or (\(x\) – 2) < 0, (\(x\) – 1) > 0 

⇒ \(x\) > 2, \(x\) < 1 or \(x\) < 2, \(x\) > 1 ⇒ \(x\) < 1 or \(x\) > 2 

∴ No value of x which lies between these extremes, i.e., 1 and 2 satisfies the inequality, i.e., 1 < \(x\) < 2 is the solution set not satisfying the inequality x² – 3\(x\) + 2 > 0 at all.